<h2>题目编号 : 91</h2>
<div style="color:#666;font-size:80%;">18 March 2005</div><br />
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<p>The points P (<i>x</i><img src="" style="display:none;" alt="_(" /><sub>1</sub><img src="" style="display:none;" alt=")" />, <i>y</i><img src="" style="display:none;" alt="_(" /><sub>1</sub><img src="" style="display:none;" alt=")" />) and Q (<i>x</i><img src="" style="display:none;" alt="_(" /><sub>2</sub><img src="" style="display:none;" alt=")" />, <i>y</i><img src="" style="display:none;" alt="_(" /><sub>2</sub><img src="" style="display:none;" alt=")" />) are plotted at integer co-ordinates and are joined to the origin, O(0,0), to form &Delta;OPQ.</p>

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<img src="project/images/p_091_1.gif" alt="" /><br />
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<p>There are exactly fourteen triangles containing a right angle that can be formed when each co-ordinate lies between 0 and 2 inclusive; that is,<br />0 <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> <i>x</i><img src="" style="display:none;" alt="_(" /><sub>1</sub><img src="" style="display:none;" alt=")" />, <i>y</i><img src="" style="display:none;" alt="_(" /><sub>1</sub><img src="" style="display:none;" alt=")" />, <i>x</i><img src="" style="display:none;" alt="_(" /><sub>2</sub><img src="" style="display:none;" alt=")" />, <i>y</i><img src="" style="display:none;" alt="_(" /><sub>2</sub><img src="" style="display:none;" alt=")" /> <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> 2.</p>

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<img src="project/images/p_091_2.gif" alt="" /><br />
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<p>Given that 0 <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> <i>x</i><img src="" style="display:none;" alt="_(" /><sub>1</sub><img src="" style="display:none;" alt=")" />, <i>y</i><img src="" style="display:none;" alt="_(" /><sub>1</sub><img src="" style="display:none;" alt=")" />, <i>x</i><img src="" style="display:none;" alt="_(" /><sub>2</sub><img src="" style="display:none;" alt=")" />, <i>y</i><img src="" style="display:none;" alt="_(" /><sub>2</sub><img src="" style="display:none;" alt=")" /> <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> 50, how many right triangles can be formed?</p>
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